The Promise Fulfilled
Lecture 1 promised: "By course end, you'll look at any chemical phenomenon and see what kind of thing it is. The math will follow."
You've built that skill.
Not memorizing tools. Seeing patterns.
The Nine Primitives
Click any primitive to explore its tools and chemistry connections.
Select a Primitive
Click above to explore
Choose a primitive from the grid above to see its associated tools, chemistry applications, and lecture connections.
The Decision Tree
When you encounter a problem, ask these questions:
Select problem characteristics above to get primitive recommendations.
Quick Tool Reference
"When do I use...?"
Dot Product
Finding angles, projections, "how much in this direction"
Cross Product
Finding perpendicular vectors, areas, torques
Eigenvalues
Finding what's preserved under transformation
Derivative
Finding instantaneous rate of change
Integral
Finding total accumulation
Differential Equation
Relating a quantity to its rate of change
Probability Distribution
Describing uncertain outcomes, populations
Dimensional Analysis
Checking equations, deriving relationships, estimating
The Course Map
Module 1: Structure
Lectures 1-10
COLLECTION
ARRANGEMENT
DIRECTION
SAMENESS
Module 2: Change
Lectures 11-19
PROXIMITY
CHANGE
RATE
ACCUMULATION
Module 3: Probability
Lectures 20-24
SPREAD
Error Analysis
Dimensions
The Method
REALITY
The phenomenon
RECOGNITION
What primitive?
TOOL
What math?
SOLUTION
Calculate
INTERPRET
Back to chemistry
Complete Reference
| Primitive | Core Tools | Key Chemistry |
|---|---|---|
| COLLECTION | Sets, factorial, combinations | Moles, configurations, isomers |
| ARRANGEMENT | Permutations, matrices | Stereochemistry, crystal structure |
| DIRECTION | Vectors, dot product | Bonds, dipoles, orbitals |
| PROXIMITY | Functions, limits | Potentials, titrations |
| SAMENESS | Eigenvalues, symmetry | Conservation, molecular symmetry |
| CHANGE | Derivatives | Rates, optimization |
| RATE | Differential equations | Kinetics, transport |
| ACCUMULATION | Integrals | Work, heat, yield |
| SPREAD | Probability, distributions | Boltzmann, quantum, error |